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In my experience GPU power requirements tend to be on the exaggerated side of things for various reasons - One of which being that overstating the power requirements makes it easier on their support, since there can be huge stability differences between a 500w psu and a ...500w psu when it comes to the amp output of the 12V rail(s) - which is basically what matters when it comes to GPUs. Writing 'requires a 'certified' 500W supply' tends to cause less confusion and hassles for the customer service than 'requires something like a quality 400W supply with >20A on the 12V rail - or a 600W aftermarket PSU that might fluctuate and actually spit out significantly less 95% of the time... you cheapskate!'.

So i'd say it boils down to the 'simple' question(s) whether the current PSU is a basically-no-name product or something like an Enermax, Antec, Be Quiet or anything along those lines, or to be more precise, how much ampere the 12v rail has (nonsense like that is always listed on the PSU itself) and how beefy and power hungry the rest of the system is.

Well, not sure if all that nonsense up there helps in any way - But to add something anecdotal and (somewhat) non-technical: I'm using a slightly overclocked 560ti which tends to have similar numbers (500-550W) listed in its requirements (and i wouldn't be surprised if it was slightly more power hungry than the 7770 (ok, some quick google-fu came up with '2-3x as power hungry'), though i'm not all that familiar with AMD cards) and my PSU (Enermax Pro-somethingsomething) is listed as 425W (22A on both 12v rails), and my GPU never complained/the system is rock solid.

Moral of the story: If it's a good PSU and the cpu isn't overclocked in a ridiculous fashion you usually can get away with at least 50-100w less than listed in the GPU requirements.

Yeah, the fact that both 12v rails are listed as 22A (and 3 and 5 at 20A) might be a bit misleading, but "misleading" seems to be the nature of the (PSU) beast in general and as far as me and my sometimes slightly warped logic can tell that simply refers to the peak output of each rail - The combined amperage of the 12v rails is 33A (for a total of 396w + 120w-ish on 3,3 and 5 - which should give rougly 425 if you squint your eyes a bit) while each rail itself has a decent bit of headroom to handle peaks. And to make things even more irritating... 425w in this particular case basically is the wattage that its always comfortable with, while its peak load is listed somewhere along the lines of 470w.

Which brings me to the PSU that you mentioned - a quick round of google-fu made it look like it's the Gigabyte SuperB 460? While it certainly doesn't fall into the aftermarket category (let's call it budget?) the mere fact that it apparently is actually a 400w PSU with a peak load of 460w basically shows the problem i mentioned in my first post - Most aftermarket and budget PSUs overstate their actual wattage and rather list the peak load than the continuous load.

But disregarding marketing nonsense for now - I actually would be surprised if the 7770 didn't run with that particular PSU - Once again pestering google with random quick queries revealed a couple of systems that include both a 7850 and that PSU, and judging by a list of power requirements for different GPUs on MSI's website lists the 7770 as having lower requirements (and a quick look at a review made it look like the 7770 consumes 80w-ish/7a-ish under heavy load?). So while i'm not able to guarantee that it will run from experience i'd say that unless there's an overclocked CPU and all sorts of power hungry nonsense in that particular rig it should be fine. But yes, PSUs are a confusing mess.

No, the numbers may be quite correct. The thing is, the PSU won't run with both 12V rails at maximum capacity. There's almost certainly going to be a lower cap for the combined 12V rails than 22A + 22A = 44A, corresponding to 528W. For example, they may be limited to a combined 400W. That each 12V rail can deliver 22A, corresponding to 264W, just means there's some wiggle room about how loads are assigned to the two rails.

I can also confirm that PSU requirements listed by AMD and Nvidia are inaccurate. They leave a very big margin for error.

As for a PSU with 15A and 14A, it should be able to feed a 7770 if the rails are set up sensibly.

It seems the Gigabyte PSU is a Gigabyte Superb 460W, which is in turn a rebranded FSP Green 400W. Yes, Gigabyte decided to label it by its peak power rating, which is dishonest. Anyway, here's a review. From 2005. Old as the hills in computing terms, but it looks alright. Should handle a 7770 fine.

Yep, those posts nicely sum up a rather lengthy post that i made earlier, which unfortunately is currently stuck in moderation and should shamelessly wedge itself into the thread in a bit. But yes, the fact that this kind of dishonesty is incredibly common when it comes to PSUs is exactly why GPU manufacturers usually make somewhat wild requirement claims - Not to mention the overall overkill trend that you often see in hardware forums. "a 560ti? at least 600w! 700w to be on the safe side"

The somewhat interesting thing about the data that you can find online is that the benchmarks that i skimmed through suggest, without exception, that the 7770 draws slightly (about 10% in both idle and under load) less power than the 450 in a 1v1 scenario. So while both choices would actually be equally risky the 7770 appears to be the safer bet (oddly enough).

True, it's not really the right word for this particular case, but "Odd" in the context of the GTS450 being listed with a 400w requirement in comparison to the 500w requirement of the 7770 - Which might make it sound like the former is the safer choice in this scenario, which would indeed be odd.